:ALRename doesn't include $ characters in input

When you use `:ALERename` the name put in the input box for renaming doesn't scan `$` characters in variable names in JavaScript and TypeScript code. We should try to implement a separate cword function that does include these characters. We should bear in mind that names may need to be handled differently for languages like PHP.

Start at the :ALERename command and inspect the existing cword input handling for JavaScript and TypeScript. Compare the naming rules needed for PHP, then verify that names containing $ are included in the rename input while existing language behavior remains correct.

Written by the indexing model from the issue text.